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The International Journal Of Engineering And Science (IJES) || Volume || 3 || Issue || 12 || December - 2014 || Pages || 48-52||ISSN (e): 2319 – 1813 ISSN (p): 2319 – 1805

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Mathematical Calculation toFindtheBest Chamber andDetectorRadii Used for Measurements theRange of α -Particle

Ali Farhan Nader, Abdul .R.H. Subber, Noori .H.N. Al-Hashimi Department of Physics; College of Education for Pure Science,University of Basra; Basra; Iraq

-------------------------------------------------------------- ABSTRACT ------------------------------------------------------- In this paper we design a new diffusion chamber which can used to record the number of alpha particle emittedby radon gas. A mathematical calculation is carried out to find the efficiency and sensitivityfor CR39 detector..The software employed is the latest version of Monte Carlo code and SRIM2013. The result shows the influenceof the initial energy on the detector parameter. Our calculations also show that, the best radius of detector is1.5 cm and the best radius of the chamber is 3.5 cm for any experimental work i.e. the chamber radius should beas twice in size as the detector radius.

KEYWORDS: detection probability, detection efficiency, CR39, LR115, Monte Carlo, SRIM2013----------------------------------------------------------------------------------------------------------------------------- ----------Date of Submission: 03November 2014 Date of Accepted: 25December 2014----------------------------------------------------------------------------------------------------------------------------- ----------

I. INTRODUCTIONSeveral techniques have been used to measure radon and its daughters. One of these techniques is the

solid state nuclear track detector SSNTDs '. Such a technique has been increasingly used in passive time-integrated modes to measure the radon and throne in the environmental medium [1]. Nuclear Track Detectors isa plastic detector uses to register alpha particles in the form of tracks. That will become visible under the opticalmicroscope upon suitable chemical etching of the SSNTDs ', the most commonly used CR-39 [2]. SSNTDs areextensively used in environmental science and technology. Polyallyl diglycol carbonate, C 12H18O7, (CR-39) andmade with cellulose nitrate materials (LR-115 II) track detectors are the most sensitive and popular detector for

recording charge particles and neutrons [3-6]. Therefore, several studies have been carried out to determine themain factors which affect the sensitivity, etching conditions and the properties of the CR-39 and LR-115 polymer as a track detector[7-15]. CR-39 is widely used detector due to its high response with low uncertaintyand suitable depth of chemical etching [16]. Any device used for relative measurement should be calibrated toconvert the device reading to the value of measurements. The response of any radon dosimeter is the calibrationfactor in track density per unit integrated concentration The calibration factor can be used to determine the radonconcentration, the mass and a real exhalation rate, the effective radium content, the radon diffusion coefficientand its diffusion length. The calibration factor or the response of SSNTDs ' has a wide range depends not only onthe geometry of the used configuration (filter and bare) but also on many parameters such as type of detector,detector efficiency and the dimension of dosimeter[17].The calibration factor may be determined experimentallyor theoretically[18,19]. Several authors have presented various calculation methods for calibration factordetermination such as analytical method, efficiency method, and the Mont Carlo method [18]. In this paperwedescribe two methods to estimate the CR-39 detector efficiency and calibration factor based on, firstly, the mean

critical angles calculation, and secondly, the Mont Carlo simulation by using the latest version of SRIM(SRIM2013) programs. A comparison between two methods is carrying on providinghigh accuracy relations.All results were compared with some experimental data.

II. THEORYThe efficiency in general can be define as the comparison of what is actually produced or performed

with what can be achieved with the same consumption of resources. It is an important factor in determinationof productivity. But in specific definition of the efficiency such as in our case, one can say is the probability ofdetection of charge particle by the detector or it is the ratio between the particles in solid angle φ to the totalsolid angle 4π.Let us assumed that a detector with area dA fixed on the surface of sphere and there is aradioactive source fixed on the center of the sphere, then by using spherical coordinate[20,21];

(1)

(2)

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According to the definition of the critical angle; , we have

(3)

or in other word (4)

where θ c is the critical angle. However some researcher used other relation for efficiency [17, 22].(5)

The detector efficiency (ε) depend on the critical angle ( θc) for track registration [18],where

The response function V(R D) (tracks etched ratio) for a certain value of R D written as.(6)

The relation between the response function and the critical angle can be written as [23]. (7)

The mean value of the critical angle written as [23](8)

Where E i the initial energy of alpha particle

III. RESULT AND DISCUSSIONTo calculate the mean critical angle one need to find analytical expression for critical angle with alpha

particle energy or any charged particle. This energy can express in term of the range of the particle in thedetector (CR39 in present case). This is possible by making use of SRIM2013 and OriginPro8 to introduce thelinear polynomial of the range versus energy.

(9)Where R(mm) the range of alpha particle , E Res(MeV) is alpha particle residual energy in the (0.1 to 10 MeV), b i (i=0...5) are fitting parameters and their values are in table (1). From equations (5-7) one can study the relation

between θc andE RES. as seen in figure (1). From this figure we can estimate an analytical relation between these parameters, which can be written as:

Where a n parameters are listed in table (2). Equation (8)that describes the mean energy canbe describe by a

polynomial form and can be written as;Table (3)

contains radon gas parameters; radon group energies and thorn group energies and the main values of θ c togetherwith the calculated values of efficiency. From figure (2) , we can see that the efficiency of the detector decreasesas the energy of the charge particle increases. The critical angle is varying from to

for CR-39 and the averge critical angle or .Tables (4-8) showthe detector efficiency for radon and throne with their progenies calculated by Monte-Carlo method. We arecalculate the efficiency together with the energy of α -particle by two difference methods that are Monte-Carlosimulation method and Mean Critical Angle method, one can conclude that the behavior of the efficiency is thesame for both methods of calculations as seen in figure (3). The calculation carried out in this work shows thatthe efficiency increases linearly with the detector diameter. Figure (4) shows that the efficiencies are almostequal if we used detector of radius 3cm, and the calculations by the two methods are combine togetherwhich isexactly equal to the range of alpha particle from radon in air. As a conclusion one can draw some points thatare: the efficiency depend on the critical angle only, the critical angle depend on the detector type and theenergy of α -particle,

Table(1-3) The best fit parameters

bo 9.51342*10 -4

b1 0.00396

b2 2.69929*10 -4

b3 1.37928*10 -4

b4 -1.42234*10 5

b5 5.04952*10 -7

Table(1)

a0 85.09436a1 -8.17899a2 3.77285

a3 -2.0352a4 0.69029a5 -0.15045a6 0.02089a7 -0.00178a8 8.46819*10 -5

a9

-1.72089*10 -6

Table(2)

Nuclide

Radon group

Rn222 5.49 71.97 34.52

Po218 6.00 70.97 33.63

Po214 7.68 67.33 30.73

Thoron group

Rn222 6.28 70.30 33.14

Po216 6.78 69.24 32.28

Bi212 6.08 70.72 33.49

Po212 8.78 64.98 28.85

Table 3

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Figure (1) CR-39 Critical angle Vs α -particle energy Figure (2) CR-39 Critical angle Vs α -particle energy

Table 7-8 The best fit arameters

Nuclide

Radon group

Rn222 5.49 35.15

Po 218 6.00 33.59

Po 214 7.68 28.21

Thoron group

Rn222 6.28 32.73

Po 216 6.78 31.28

Bi212

6.08 33.35Po 212 8.78 24.75

Table 7

Nuclide

Radongroup 0.33 0.32 0.22 0.14 0.13

Thoron

group 0.49 0.46 0.31 0.19 0.17

Table 8

Table(4-6) The best fit parameters

Nuclide

Radon group

Rn222 5.49 15.88

Po 218 6.00 14.09

Po214

7.68 9.82Thoron group

Rn222 6.28 13.21

Po 216 6.78 11.82

Bi 212 6.08 13.83

Po 212 8.78 7.98

Table 4

Nuclide

Radon group

Rn222 5.49 26.64

Po 218 6.00 24.42

Po214

7.68 18.03Thoron group

Rn222 6.28 23.22

Po 216 6.78 21.18

Bi 212 6.08 24.07

Po 212 8.78 14.95Table 5

Nuclide

Radon group

Rn 222 5.49 26.64

Po 218 6.00 24.42

Po214

7.68 18.03Thoron group

Rn 222 6.28 23.22

Po 216 6.78 21.18

Bi 212 6.08 24.07

Po 212 8.78 14.95

Table 6

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4. ConclusionThe radon atoms inside the chamber can decay and create new progeny, which mayfurther decay whilst

in the air volume of the chamber or after their deposition on the chamberwall. There are three types of alpha- particle emitters in air (Rn, non-deposited fraction ofPo and Po), and those on the chamber wall (depositedfractionPo and Po) and emitters deposited on the detector itself(plate outPo and Po). Based on the above onecan conclude that the calculations by two method are almost the same when the detector radius equal 3 cm. Wefind that the best radius of detector is 1.5 cm and the best radius of the chamber is 3.5 cm for any experimentalwork i.e. the chamber radius should be twice in size as the detector radius.

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Figure (3) CR-39 efficiency Vs α -particle initial energyBy using Mount-Carlo method only

Figure (4) efficiency Vs α -particle initial energyBy using Mount-Carlo and Mean Critical angle method

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